What do the following two equations represent? $x-2y = 4$ $6x+3y = 1$
Answer: Putting the first equation in $y = mx + b$ form gives: $x-2y = 4$ $-2y = -x+4$ $y = \dfrac{1}{2}x - 2$ Putting the second equation in $y = mx + b$ form gives: $6x+3y = 1$ $3y = -6x+1$ $y = -2x + \dfrac{1}{3}$ The slopes are negative inverses of each other, so the lines are perpendicular.